With the summit – dubbed in advance a “moment of truth” for Brexit - wrapping up in disappointment without a deal again, Mrs May admitted yesterday that “here is a lot of hard work ahead”.

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French President Emmanuel Macron, seen here with Michel Barnier, has been one of the harshest critics of Mrs May's proposalsCredit: Reuters

She added: “There will be more difficult moments as we enter the final stages of the talks, but I'm convinced we will secure a good deal”.

Quizzed by The Sun yesterday on what had gone at home and abroad, the PM insisted: “These were always going to be tough negotiations, and they were always going to get tougher as we got to the closing stages”.

An extension could be useful as “a further solution” to the Irish dilemma, she also said, as living a bit longer under EU rules until a trade deal is agreed would mean the hated Irish backstop that keeps Britain within an EU custons union would then never have to kick in.

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German Chancellor Angela Merkel has seemed to have softened her position on BrexitCredit: Getty - Contributor

But Downing Street could not rule out having to fork out billions to stay under EU rules for longer, or that it would have any time limit.

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“However it doesn't have a hope in hell in getting through unless it replaces the Northern Ireland only bit."

A senior Government source added: “We need something to get the talks going again. If extending transition is an option they want to look at, we must go along with that. For us to say at this point that we’re not listening would not have been very sensible.”

Business bosses backed a longer transition if it meant getting a deal.

CBI Director-General Carolyn Fairbairn said: “Business’ patience was already threadbare and is nearing an end. The need for compromise on both sides to agree the Withdrawal Agreement and secure the transition period is long overdue.

CAINE IN SHOW OF SUPPORT

FILM legend Sir Michael Caine yesterday predicted furious business chiefs would force the EU to strike a Brexit deal.

The multi-millionaire actor, 85, insisted he still believes in Brexit.

He said it was better for the UK to be in charge of its own destiny than in hock to Eurocrats.

In a BBC interview he said: “I’d rather be a poor master of my fate than having someone I don’t know making me rich by running it.”

He suggested German car companies were the key to trade deals.

The chief economist at Germany’s biggest bank has predicted the UK would thrive after Brexit.

Deutsche Bank’s David Folkerts-Landau said yesterday Britain would do “just as well or better” after it leaves the EU.

PM Theresa May claims Irish border 'backstop' WILL be temporary and there has been 'real progress' during Brexit statement